Because a double negative = a positive.
'Elephants are grey' = positive
'Elephants are not grey. = negative
Elephants are not not grey.' = double negative = elephants are grey
If something is not not something, then it is that thing. 'Negative' is basically another way of saying 'opposite': imagine the number 2 sees itself in a mirror. The number 2 is 2 units away from zero. The number minus 2 is 2 units away from zero, but in the opposite direction.
So -2*-2 = - - 4, i.e. the opposite of minus 4. The opposite of -4 is 4.